Monthly Archives: October 2015

Humanists know the subjects we study are complex. So on the rare occasions when we describe them with numbers at all, we tend to proceed cautiously. Maybe too cautiously. Distant readers have spent a lot of time, for instance, just convincing colleagues that it might be okay to use numbers for exploratory purposes.

But the pace of this conversation is not entirely up to us. Outsiders to our disciplines may rush in where we fear to tread, forcing us to confront questions we haven’t faced squarely.

For instance, can we use numbers to identify historical periods when music or literature changed especially rapidly or slowly? Humanists have often used qualitative methods to make that sort of argument. At least since the nineteenth century, our narratives have described periods of stasis separated by paradigm shifts and revolutionary ruptures. For scientists, this raises an obvious, tempting question: why not actually measure rates of change and specify the points on the timeline when ruptures happened?

When disciplinary outsiders make big historical claims, humanists may be tempted just to roll our eyes. But I don’t think this is a kind of intervention we can afford to ignore. Arguments about the pace of cultural change engage theoretical questions that are fundamental to our disciplines, and questions that genuinely fascinate the public. If scientists are posing these questions badly, we need to explain why. On the other hand, if outsiders are addressing important questions with new methods, we need to learn from them. Scholarship is not a struggle between disciplines where the winner is the discipline that repels foreign ideas with greatest determination.

I feel particularly obligated to think this through, because I’ve been arguing for a couple of years that quantitative methods tend to reveal gradual change rather than the sharply periodized plateaus we might like to discover in the past. But maybe I just haven’t been looking closely enough for discontinuities? Recent articles introduce new ways of locating and measuring them.

This blog post applies methods from “The evolution of popular music” to a domain I understand better — nineteenth-century literary history. I’m not making a historical argument yet, just trying to figure out how much weight these new methods could actually support. I hope readers will share their own opinions in the comments. So far I would say I’m skeptical about these methods — or at least skeptical that I know how to interpret them.

How scientists found musical revolutions.

Mauch et al. start by collecting thirty-second snippets of songs in the Billboard Hot 100 between 1960 and 2010. Then they topic-model the collection to identify recurring harmonic and timbral topics. To study historical change, they divide the fifty-year collection into two hundred quarter-year periods, and aggregate the topic frequencies for each quarter. They’re thus able to create a heat map of pairwise “distances” between all these quarter-year periods. This heat map becomes the foundation for the crucial next step in their argument — the calculation of “Foote novelty” that actually identifies revolutionary ruptures in music history.

The diagonal line from bottom left to top right of the heat map represents comparisons of each time segment to itself: that distance, obviously, should be zero. As you rise above that line, you’re comparing the same moment to quarters in its future; if you sink below, you’re comparing it to its past. Long periods where topic distributions remain roughly similar are visible in this heat map as yellowish squares. (In the center of those squares, you can wander a long way from the diagonal line without hitting much dissimilarity.) The places where squares are connected at the corners are moments of rapid change. (Intuitively, if you deviate to either side of the narrow bridge there, you quickly get into red areas. The temporal “window of similarity” is narrow.) Using an algorithm outlined by Jonathan Foote (2000), the authors translate this grid into a line plot where the dips represent musical “revolutions.”

Trying the same thing on the history of the novel.

Could we do the same thing for the history of fiction? The labor-intensive part would be coming up with a corpus. Nineteenth-century literary scholars don’t have a Billboard Hot 100. We could construct one, but before I spend months crafting a corpus to address this question, I’d like to know whether the question itself is meaningful. So this is a deliberately rough first pass. I’ve created a sample of roughly 1000 novels in a quick and dirty way by randomly selecting 50 male and 50 female authors from each decade 1820-1919 in HathiTrust. Each author is represented in the whole corpus only by a single volume. The corpus covers British and American authors; spelling is normalized to modern British practice. If I were writing an article on this topic I would want a larger dataset and I would definitely want to record things like each author’s year of birth and nationality. This is just a first pass.

Because this is a longer and sparser sample than Mauch et al. use, we’ll have to compare two-year periods instead of quarters of a year, giving us a coarser picture of change. It’s a simple matter to run a topic model (with 50 topics) and then plot a heat map based on cosine similarities between the topic distributions in each two-year period.

Voila! The dark and light patterns are not quite as clear here as they are in “The evolution of popular music.” But there are certainly some squarish areas of similarity connected at the corners. If we use Foote novelty to interpret this graph, we’ll have one major revolution in fiction around 1848, and a minor one around 1890. (I’ve flipped the axis so peaks, rather than dips, represent rapid change.) Between these peaks, presumably, lies a valley of Victorian stasis.

Is any of that true? How would we know? If we just ask whether this story fits our existing preconceptions, I guess we could make it fit reasonably well. As Eleanor Courtemanche pointed out when I discussed this with her, the end of the 1840s is often understood as a moment of transition to realism in British fiction, and the 1890s mark the demise of the three-volume novel. But it’s always easy to assimilate new evidence to our preconceptions. Before we rush to do it, let’s ask whether the quantitative part of this argument has given us any reason at all to believe that the development of English-language fiction really accelerated in the 1840s.

I want to pose four skeptical questions, covering the spectrum from fiddly quantitative details to broad theoretical doubts. I’ll start with the fiddliest part.

1) Is this method robust to different ways of measuring the “distance” between texts?

The short answer is “yes.” The heat maps plotted above are calculated on a topic model, after removing stopwords, but I get very similar results if I compare texts directly, without a topic model, using a range of different distance metrics. Mauch et al. actually apply PCA as well as a topic model; that doesn’t seem to make much difference. The “moments of revolution” stay roughly in the same place.

2) How crucial is the “Foote novelty” piece of the method?

Very crucial, and this is where I think we should start to be skeptical. Mauch et al. are identifying moments of transition using a method that Jonathan Foote developed to segment audio files. The algorithm is designed to find moments of transition, even if those moments are quite subtle. It achieves this by making comparisons — not just between the immediately previous and subsequent moments in a stream of observations — but between all segments of the timeline.

It’s a clever and sensitive method. But there are other, more intuitive ways of thinking about change. For instance, we could take the first ten years of the dataset as a baseline and directly compare the topic distributions in each subsequent novel back to the average distribution in 1820-1829. Here’s the pattern we see if we do that:

That looks an awful lot like a steady trend; the trend may gradually flatten out (either because change really slows down or, more likely, because cosine distances are bounded at 1.0) but significant spurts of revolutionary novelty are in any case quite difficult to see here.

That made me wonder about the statistical significance of “Foote novelty,” and I’m not satisfied that we know how to assess it. One way to test the statistical significance of a pattern is to randomly permute your data and see how often patterns of the same magnitude turn up. So I repeatedly scrambled the two-year periods I had been comparing, constructed a heat matrix by comparing them pairwise, and calculated Foote novelty.

A heatmap produced by randomly scrambling the fifty two-year periods in the corpus. The “dates” on the timeline are now meaningless.

When I do this I almost always find Foote novelties that are as large as the ones we were calling “revolutions” in the earlier graph.

The authors of “The evolution of popular music” also tested significance with a permutation test. They report high levels of significance (p < 0.01) and large effect sizes (they say music changes four to six times faster at the peak of a revolution than at the bottom of a trough). Moreover, they have generously made their data available, in a very full and clearly-organized csv. But when I run my permutation test on their data, I run into the same problem — I keep discovering random Foote novelties that seem as large as the ones in the real data.

It’s possible that I’m making some error, or that we're testing significance differently. I'm permuting the underlying data, which always gives me a matrix that has the checkerboardy look you see above. The symmetrical logic of pairwise comparison still guarantees that random streaks organize themselves in a squarish way, so there are still “pinch points” in the matrix that create high Foote novelties. But the article reports that significance was calculated “by random permutation of the distance matrix.” If I actually scramble the rows or columns of the distance matrix itself I get a completely random pattern that does give me very low Foote novelty scores. But I would never get a pattern like that by calculating pairwise distances in a real dataset, so I haven’t been able to convince myself that it’s an appropriate test.

3) How do we know that all forms of change should carry equal cultural weight?

Now we reach some questions that will make humanists feel more at home. The basic assumption we’re making in the discussion above is that all the features of an expressive medium bear historical significance. If writers replace “love” with “spleen,” or replace “cannot” with “can’t,” it may be more or less equal where this method is concerned. It all potentially counts as change.

This is not to say that all verbal substitutions will carry exactly equal weight. The weight assigned to words can vary a great deal depending on how exactly you measure the distance between texts; topic models, for instance, will tend to treat synonyms as equivalent. But — broadly speaking — things like contractions can still potentially count as literary change, just as instrumentation and timbre count as musical change in “The evolution of popular music.”

At this point a lot of humanists will heave a relieved sigh and say “Well! We know that cultural change doesn’t depend on that kind of merely verbal difference between texts, so I can stop worrying about this whole question.”

Not so fast! I doubt that we know half as much as we think we know about this, and I particularly doubt that we have good reasons to ignore all the kinds of change we’re currently ignoring. Paying attention to merely verbal differences is revealing some massive changes in fiction that previously slipped through our net — like the steady displacement of abstract social judgment by concrete description outlined by Heuser and Le-Khac in LitLab pamphlet #4.

For me, the bottom line is that we know very little about the kinds of change that should, or shouldn’t, count in cultural history. “The evolution of popular music” may move too rapidly to assume that every variation of a waveform bears roughly equal historical significance. But in our daily practice, literary historians rely on a set of assumptions that are much narrower and just as arbitrary. An interesting debate could take place about these questions, once humanists realize what’s at stake, but it’s going to be a thorny debate, and it may not be the only way forward, because …

4) Instead of discussing change in the abstract, we might get further by specifying the particular kinds of change we care about.

Our systems of cultural periodization tend to imply that lots of different aspects of writing (form and style and theme) all change at the same time — when (say) “aestheticism” is replaced by “modernism.” That underlying theory justifies the quest for generalized cultural growth spurts in “The evolution of popular music.”

But we don’t actually have to think about change so generally. We could specify particular social questions that interest us, and measure change relative to those questions.

The advantage of this approach is that you no longer have to start with arbitrary assumptions about the kind of “distance” that counts. Instead you could use social evidence to train a predictive model. Insofar as that model predicts the variables you care about, you know that it’s capturing the specific kind of change that matters for your question.

Jordan Sellers and I took this approach in a working paper we released last spring, modeling the boundary between volumes of poetry that were reviewed in prominent venues, and those that remained obscure. We found that the stylistic signals of poetic prestige remained relatively stable across time, but we also found that they did move, gradually, in a coherent direction. What we didn’t do, in that article, is try to measure the pace of change very precisely. But conceivably you could, using Foote novelty or some other method. Instead of creating a heatmap that represents pairwise distances between texts, you could create a grid where models trained to recognize a social boundary in particular decades make predictions about the same boundary in other decades. If gender ideologies or definitions of poetic prestige do change rapidly in a particular decade, it would show up in the grid, because models trained to predict authorial gender or poetic prominence before that point would become much worse at predicting it afterward.

Conclusion

I haven’t come to any firm conclusion about “The evolution of popular music.” It’s a bold article that proposes and tests important claims; I’ve learned a lot from trying the same thing on literary history. I don’t think I proved that there aren’t any revolutionary growth spurts in the history of the novel. It’s possible (my gut says, even likely) that something does happen around 1848 and around 1890. But I wasn’t able to show that there’s a statistically significant acceleration of change at those moments. More importantly, I haven’t yet been able to convince myself that I know how to measure significance and effect size for Foote novelty at all; so far my attempts to do that produce results that seem different from the results in a paper written by four authors who have more scientific training than I do, so there’s a very good chance that I’m misunderstanding something.

I would welcome comments, because there are a lot of open questions here. The broader task of measuring the pace of cultural change is the kind of genuinely puzzling problem that I hope we’ll be discussing at more length in the IPAM Cultural Analytics workshop next spring at UCLA.

Postscript Oct 5: More will be coming in a day or two. The suggestions I got from comments (below) have helped me think the quantitative part of this through, and I’m working up an iPython notebook that will run reliable tests of significance and effect size for the music data in Mauch et al. as well as a larger corpus of novels. I have become convinced that significance tests on Foote novelty are not a good way to identify moments of rapid change. The basic problem with that approach is that sequential datasets will always have higher Foote novelties than permuted (non-sequential) datasets, if you make the “window” wide enough — even if the pace of change remains constant. Instead, borrowing an idea from Hoyt Long and Richard So, I’m going to use a Chow test to see whether rates of change vary.

Postscript Oct 8: Actually it could be a while before I have more to say about this, because the quantitative part of the problem turns out to be hard. Rates of change definitely vary. Whether they vary significantly, may be a tricky question.